The equality conditions in Suita's Theorem (Theorem REF ) and in \(c_\beta \ge c_B\)  (Theorem REF ) imply that the equality condition in Case 1 holds if and only if \(\Omega \)  is biholomorphic to a disk less a relatively closed polar set. Since \(\Omega \)  is Lipschitz, it is a regular domain for the Dirichlet problem. Thus, the polar set is empty, cf. [1]}.
